On an inverse scattering problem for a class Dirac operator with discontinuous coefficient and nonlinear dependence on the spectral parameter in the boundary condition

Mamedov K.R.; ??l A.

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On an inverse scattering problem for a class Dirac operator with discontinuous coefficient and nonlinear dependence on the spectral parameter in the boundary condition

机译：边界条件下具有不连续系数和非线性依赖谱参数的一类Dirac算子的逆散射问题

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On the positive semi-infinite interval, we obtained a generalization of the Marchenko method for a Dirac equation system with a discontinuous coefficient and a quadratic polynomial on a spectral parameter in the boundary condition. In this connection, we use an new integral representation of the Jost solution of equation systems, which does not have a 'triangular' form. The scattering function of the problem is defined, and its properties are examined. The Marchenko-type main equation is obtained, and it is shown that the potential is uniquely recovered in terms the scattering function.

机译：在正半无限区间上，我们获得了在边界条件下具有谱参数的不连续系数和二次多项式的Dirac方程组的Marchenko方法的推广。在这方面，我们使用方程系统的Jost解的新积分表示形式，该形式不具有“三角”形式。定义了问题的散射函数，并研究了其性质。得到了马尔琴科型主方程，并且表明，就散射函数而言，电势是唯一恢复的。

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《Mathematical Methods in the Applied Sciences》 |2012年第14期|共9页
作者
Mamedov K.R.; ??l A.;
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正文语种 eng
中图分类数学;
关键词
Dirac equation system; discontinuous coefficient; Marchenko-type equation; nonlinear spectral parameter; scattering function;

机译：Dirac方程组;间断系数;Marchenko型方程;非线性光谱参数;散射函数;

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专利

1. On an inverse scattering problem for a class Dirac operator with discontinuous coefficient and nonlinear dependence on the spectral parameter in the boundary condition [J] . Mamedov K.R., ??l A. Mathematical Methods in the Applied Sciences . 2012,第14期

机译：边界条件下具有不连续系数和非线性依赖谱参数的一类Dirac算子的逆散射问题
2. On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition [J] . ??l A., Mamedov K. Journal of Mathematical Analysis and Applications . 2012,第2期

机译：边界条件下带谱参数的一类Dirac算子的逆散射问题
3. Inverse scattering problem for Sturm-Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition [J] . Mamedov Kh.R., Kosar N.P. Mathematical Methods in the Applied Sciences . 2011,第2期

机译：边界条件下与光谱参数非线性相关的Sturm-Liouville算子的逆散射问题
4. Inverse scattering problem for the non-stationary matrix Dirac equation on the half-plane with the singular transmission matrix in the boundary condition [C] . Ibrahim Tekin, Mansur I. Ismailov International Conference on Advancements in Mathematical Sciences . 2015

机译：边界条件下奇异传输矩阵的半平面上非静止矩阵DIRAC方程的逆散射问题
5. Inverse Scattering Transform and Solitons for Matrix Nonlinear Schr?dinger Systems and for the Defocusing Ablowitz-Ladik Equation with Nonzero Boundary Conditions [D] . Ortiz, Alyssa Kayelin. 2019

机译：逆散射变换和矩阵非线性SCHR？Dinger系统以及与非零边界条件的Defocusing Ablowitz-Ladik方程
6. Subelliptic boundary conditions for Spinℂ–Dirac operators gluing relative indices and tame Fredholm pairs [O] . Charles L. Epstein 2006

机译：Spinℂ–Dirac算子的次椭圆边界条件胶合相对指数和驯服的Fredholm对
7. On an inverse problem for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition [O] . Mamedov Kh. R., ??l Aynur 2010

机译：边界条件下具有不连续系数和谱参数的Dirac算子的逆问题
8. Estimation of Discontinuous Coefficients and Boundary Parameters for Hyperbolic Systems. [R] . Lamm, P. K., Murphy, K. A. 1988

机译：双曲系统的间断系数和边界参数估计。

On an inverse scattering problem for a class Dirac operator with discontinuous coefficient and nonlinear dependence on the spectral parameter in the boundary condition

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